Question

if x < y, prove that -y < -x

Answer 1

what properties are available?

Answer 2

(P1) : a +(b+c) = (a+b)+c
(P2): a + (-a) = (-a) + a = 0
(P3): a + 0 = 0 + a = a
(P4): a +b = b + a
(P5): a(bc) = (ab)c

Answer 3

ok. what is definition of "<"

Answer 4

x<y
x+(-x)<y+(-x)
0<y+(-x)
-y<y+(-y)-x
-y<-x

Answer 5

good use of properties there